The value of a piano is one of the hardest questions to answer as there are many variables, from the local economy to the availability in your area, what brand it is, what the cosmetic condition is, what the playable condition is, to name a few. For the average piano you should probably do some online research into the brand of the piano and see what the going rate is on pianos of equal condition and quality in your area.
The age of a piano is not always easy to tell. The piano action for the last hundred+ years has not really changed in design making it difficult to tell by the internals just how old it is. The design of the piano cabinet can give some clues though, during different decades different types of wood have been more popular than others and older pianos from the early 1900's and before were usually much more ornate with carvings. The best way to tell the age of a piano is by a search of the serial number. The Pierce Piano Atlas is a good resource for this with information on more than 12,000 brand names.
A sticking piano key is a very common problem, however, it does not always have a common cause. From tight balance rail or front rail pins, to warped keys, to all manner of foreign objects that can get inside the piano, there is no one single answer to the sticking key. The only way to know for sure is to have a technician come out and take a look at the piano.